Semileptonic decays of $D_{(s)}$ mesons

Abstract

A symmetry-preserving continuum approach to meson bound-states in quantum field theory, employed elsewhere to describe numerous $\pi$- and $K$-meson electroweak processes, is used to analyse leptonic and semileptonic decays of $D_{(s)}$ mesons. Each semileptonic transition is conventionally characterised by the value of the dominant form factor at $t=0$ and the following results are obtained herein: $f_{+}^{D_s\to K}(0)=0.673(40)$; $f_{+}^{D\to \pi }(0)=0.618(31)$; and $f_{+}^{D\to K}(0)=0.756(36)$. Working with the computed $t$-dependence of these form factors and standard averaged values for $|V_{cd}|$, $|V_{cs}|$, one arrives at the following predictions for the associated branching fractions: ${\mathcal{B}}_{D_s^{+}\to K^0{e}^{+}{\nu }_e}=3.31(33)\times 10^{-3}$; ${\mathcal{B}}_{D^0\to {\pi }^{-}{e}^{+}{\nu }_e}=2.73(22)\times 10^{-3}$; and ${\mathcal{B}}_{D^0\to K^{-}{e}^{+}{\nu }_e}=3.83(28)$%. Alternatively, using the calculated $t$-dependence, agreement with contemporary empirical results for these branching fractions requires $|V_{cd}|=0.221(9)$, $|V_{us}|=0.953(34)$. With all $D_{(s)}$ transition form factors in hand, the nature of SU$(3)$-flavour symmetry-breaking in this array of processes can be analysed; and just as in the $\pi$-$K$ sector, the magnitude of such effects is found to be determined by the scales associated with emergent mass generation in the Standard Model, not those originating with the Higgs mechanism.

arXiv comment9 pages, 5 figures, 4 tables

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